Methods, apparatus and articles of manufacture to process cardiac images to detect heart motion abnormalities

ABSTRACT

Example methods, apparatus and articles of manufacture to process cardiac images to detect heart motion abnormalities are disclosed. A disclosed example method includes using a filter coefficient based on a plurality of cardiac images to characterize motion of a heart; computing an information-theoretic metric from the filter coefficient; and comparing the information-theoretic metric to a threshold to determine whether the motion of the heart is abnormal.

RELATED APPLICATION

This patent arises from a continuation of U.S. patent application Ser.No. 12/633,519, filed on Dec. 8, 2009, now U.S. Pat. No. 8,478,012,issued on Jul. 2, 2013, which claims benefit from U.S. ProvisionalPatent Application Ser. No. 61/242,215, entitled “Methods, Apparatus andArticles of Manufacture to Detect Heart Motion Abnormalities,” and filedSep. 14, 2009. U.S. patent application Ser. No. 12/633,519 and U.S.Provisional Patent Application Ser. No. 61/242,215 are herebyincorporated by reference herein in their entireties.

FIELD OF THE DISCLOSURE

This disclosure relates generally to cardiac images and, moreparticularly, to methods, apparatus and articles of manufacture toprocess cardiac images to detect heart motion abnormalities.

BACKGROUND

A widely used cardiac diagnostic technique involves the imaging ofdifferent portions of a heart during various phases of a heartbeat orcardiac cycle to detect or diagnose cardiac disease, abnormalitiesand/or damage. Example cardiac imaging tools are a magnetic resonanceimaging (MRI) system and a computed topography (CT) imaging system.

BRIEF DESCRIPTION OF THE INVENTION

In view of the following descriptions and figures, it should be clearthat the present disclosure describes methods, apparatus and articles ofmanufacture to process cardiac images to detect heart motionabnormalities. Coronary heart disease is the most common type ofcardiovascular disease, and early detection of heart motionabnormality(-ies) may be used to diagnose and/or control heart disease.Accordingly, quantitative scoring of heart wall motion may be extremelyuseful in the clinical environment. However, due to the vast amount ofinformation and uncertainty associated with heart motion, earlydetection of heart motion abnormalities may be difficult via visualinspection of cardiac images.

The example methods, apparatus and articles of manufacture disclosedherein provide certain advantages over existing heart motionclassification methods. For example, the subjective evaluation of heartimages by a radiologist can be reduced and/or eliminated, therebyreducing inter and/or intra-observer variability. The examples disclosedherein also enabled automated analysis, which can reduce the timerequired to obtain a diagnosis and/or begin treatment.

As disclosed herein, left-ventricle heart motion abnormalities may bedetected by processing a sequence of cardiac images. The cardiac imagesmay be segmented into one or more regions, and then processed orfiltered with a cyclic model such as a recursive Bayesian filter or aKalman filter. An example segmented region corresponds to theleft-ventricular heart cavity. The cyclic model may be adapted and/oradjusted to apply temporal smoothing to the segmented cardiac images ofthe left-ventricular heart cavity. Such smoothing may be used to reducethe effect of image noise and/or segmentation inaccuracies. Statesand/or coefficients of the cyclic model may be used to characterizeand/or represent the dynamics and/or motion of the segmentleft-ventricular heart cavity.

Due to statistical similarity between normal and abnormal hearts, theclassification and/or discrimination of heart motion based ondistribution moments such as the mean systolic velocity may be difficultand/or inaccurate. Instead, an information-theoretic measure or metricof left-ventricle wall motion may be computed from the cyclic modelstates and/or coefficients. An example information-theoretic metriccomprises the Shannon differential entropy (SDE), which provides aglobal theoretically-grounded measure of statistical distributions and,thus, may be used to accurately discriminate between different types ofheart motion. Other example information-theoretic metrics include, butare not limited to, the Rényi entropy and Fisher information. Theinformation-theoretic metric may be compared to decision criteria todetermine whether the heart motion depicted in the cardiac images isnormal or abnormal.

According to certain aspects of this disclosure, an example methodincludes adapting a state of a state-space model based on a plurality ofcardiac images to characterize motion of a heart, computing aninformation-theoretic metric from the state of the state-space model,and comparing the information-theoretic metric to a threshold todetermine whether the motion of the heart is abnormal.

According to further aspects of this disclosure, an example apparatusincludes a motion estimator to adapt a state of a state-space modelbased on a plurality of cardiac images to characterize motion of aheart, an information metric processor to compute aninformation-theoretic metric from the state of the state-space model,and a classifier to compare the information-theoretic metric to athreshold to determine whether the motion of the heart is abnormal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of an example diagnostic imagingsystem within which the example methods, apparatus and articles ofmanufacture described herein may be implemented.

FIG. 2 illustrates an example image lifecycle management flow withinwhich the example methods, apparatus and articles of manufacturedescribed herein may be implemented.

FIG. 3 illustrates an example manner of implementing the examplediagnostic workstation of FIG. 1.

FIG. 4 illustrates an example manner of implementing the example imageprocessing module of FIG. 3.

FIG. 5 is a flowchart representative of example process that may becarried out to implement the example diagnostic workstation of FIGS. 1and 3.

FIG. 6 is a schematic illustration of an example processor platform thatmay be used and/or programmed to carry out the example process of FIG. 5and/or to implement any or all of the example methods, apparatus andarticles of manufacture described herein.

DETAILED DESCRIPTION

In the interest of brevity and clarity, throughout the followingdisclosure references will be made to an example diagnostic imagingworkstation 105. However, the methods, apparatus and articles ofmanufacture described herein to process cardiac left-ventricle images todetect heart motion abnormalities may be implemented by and/or withinany number and/or type(s) of additional and/or alternative diagnosticimaging systems. For example, the methods, apparatus and articles ofmanufacture described herein could be implemented by or within a deviceand/or system that captures diagnostic images (e.g., a computedtomography (CT) imaging system and/or magnetic resonance imaging (MRI)system), and/or by or within a system and/or workstation designed foruse in viewing, analyzing, storing and/or archiving diagnostic images(e.g., the GE® picture archiving and communication system (PACS), and/orthe GE advanced workstation (AW)). Moreover, the example methods,apparatus and articles of manufacture disclosed herein may be used toprocess any number and/or type(s) of other images, including other typesof cardiac images, to detect motion abnormalities.

FIG. 1 illustrates an example diagnostic imaging system 100 includingthe example diagnostic imaging workstation 105 to process cardiacleft-ventricle images to detect heart motion abnormalities. The cardiacleft-ventricle images may be captured by any number and/or type(s) ofimage acquisition system(s) 110, and stored in any number and/or type(s)of image database(s) 115 managed by any number and/or type(s) of imagemanager(s) 120. The processing of cardiac left-ventricle images by theexample diagnostic imaging workstation 105 may be scheduled by anynumber and/or type(s) of scheduler(s) 125. Example image acquisitionsystems 110 include, but are not limited to, a CT imaging system and/oran MRI system. Images may be stored and/or archived in the example imagedatabase 115 of FIG. 1 using any number and/or type(s) of datastructures, and the example image database 115 may be implemented usingany number and/or type(s) of memory(-ies), memory device(s) and/orstorage device(s) such as a hard disk drive, a compact disc (CD), adigital versatile disc (DVD), a floppy drive, etc.

FIG. 2 illustrates an example image lifecycle management flow 200 thatmay be implemented by the example diagnostic imaging system 100 ofFIG. 1. Images (e.g., left-ventricle images) are acquired, createdand/or modified by the image acquisition system(s) 110. The imagemanager(s) 120 replicate, distribute, organize and/or otherwise managethe captured images. The example diagnostic imaging workstation 105 ofFIG. 1 processes a sequence of replicated, distributed, organized and/orotherwise managed images to, among other things, detect heart motionabnormalities. Information created, computed and/or otherwise determinedduring the classification and/or detection of heart motion by thediagnostic imaging workstation 105 can be used to reduce the number ofimage(s) and/or the amount of data that must be stored, archived and/orotherwise maintained for future recall.

FIG. 3 is a schematic illustration of an example diagnostic imagingworkstation 105 within which the example methods, apparatus and articlesof manufacture to detect heart motion abnormalities described herein maybe implemented. To allow a user (not shown) to interact with the examplediagnostic imaging workstation 105 of FIG. 3, the diagnostic imagingworkstation 105 includes any number and/or type(s) of user interfacemodule(s) 305, any number and/or type(s) of display(s) 310 and anynumber and/or type(s) of input device(s) 315. The example user interfacemodule(s) 305 of FIG. 3 implements an operating system to presentinformation (e.g., images, windows, screens, interfaces, dialog boxes,etc.) at the display(s) 310, and to allow a user to control, configureand/or operate the example diagnostic imaging workstation 105. The userprovides and/or makes inputs and/or selections to the user interfacemodule 305 and/or, more generally, to the example diagnostic imagingworkstation 105 via the input device(s) 315. Example input devices 315include, but are not limited to, a keyboard, a touch screen and/or amouse. In an example, a patient search window is presented at thedisplay 310, and the input device(s) 315 are used to enter searchcriteria to identify a particular patient. When a patient is identifiedand selected, the example user interface 305 presents a list ofavailable diagnostic images for the patient at the display 310, and theuser selects one or more sequences of diagnostic images using the inputdevice(s) 315. The user interface 305 then obtains the selected imagesequence(s) from the example image manager 120. An image-processingmodule 325 processes the selected image sequence(s) to determine whetherany heart motion abnormalities are present, and presents informationrelated to the presence or absence of heart motion abnormalities at thedisplay 310 for viewing by the user. An example manner of implementingthe example image processing module 325 is described below in connectionwith FIG. 4.

In the illustrated example of FIG. 3, selected image sequence(s) arepre-processed by an image pre-processing module 320 before processing bythe example image-processing module. Using any number and/or type(s) ofmethod(s) and/or algorithm(s), the example image pre-processing module320 of FIG. 3 processes the selected images to detect the boundary ofthe left-ventricle heart cavity in each selected image. In other words,the example pre-processing module 320 processes the selected images toidentify the endocardium in each of the selected images. Example systemsand methods for pre-processing images are described in U.S. patentapplication Ser. No. 12/325,226, filed on Nov. 30, 2008, now U.S. Pat.No. 8,144,930, and entitled “Systems and Methods For Tracking Images,”which is hereby incorporated by reference in its entirety.

Let I represent a cardiac sequence containing K frames I^(k):Ω⊂

²→

⁺, kε[1, . . . , K]. The example pre-processing module 320 of FIG. 3preprocesses the set of images I to detect the boundary of theleft-ventricle cavity of the heart (the endocardium) in each frame kε[2,. . . , K]. The example pre-processing module 320 determines theboundary of the endocardium by evolving a closed planar parametric curve{right arrow over (Γ)}^(k)(s):[0,1]→Ω toward the endocardium. In someexamples, the parametric curve {right arrow over (Γ)}^(k) is evolved byminimizing a cost function F^(k) that includes, among other things, anoverlap-prior term or constraint that prevents the papillary muscles ofthe left-ventricle cavity from being included erroneously in the heartmyocardium. However, because the papillary muscles and the myocardiumare connected and have almost the same intensity profile theirseparation may be difficult. Minimization of the cost function F^(k)results in each frame k being segmented into two regions: theleft-ventricle cavity C^(k) corresponding to the interior of theparametric curve {right arrow over (Γ)}^(k)C ^(k) =

  (1)where R_({right arrow over (Γ)}) denotes the region enclosed by curve{right arrow over (Γ)}, and the background B^(k) corresponding to theregion outside the parametric curve {right arrow over (Γ)}^(k),B ^(k) =

  (2)An example cost functional F^(k) includes three terms: an overlap-priorterm, a mean-matching term and a regularization/gradient term, which aredefined as follows.

An example overlap-prior term is defined using the followingdefinitions. P_(R,I) is the nonparametric (kernel-based) estimate of theintensity distribution within region R in frame Iε{I^(k), k=1, . . . ,K}

$\begin{matrix}{{\forall{z \in {\mathbb{R}}^{+}}},{{P_{R,I}(z)} = \frac{\int_{R}{{K\left( {\Sigma - {l(x)}} \right)}\ {\mathbb{d}x}}}{a_{R}}},} & (3)\end{matrix}$where a_(R) is the area of region Ra _(R)=∫_(R) dx  (4)Example kernels K(•) include, but are not limited to, the Dirac functionand the Gaussian kernel. B(f/g) is the Bhattacharyya coefficientrepresenting the amount of overlap between two statistical samples f andgB(f/g)=Σ_(zεR) ₊ √{square root over (f(z)g(z))}{square root over(f(z)g(z))}  (5)In the examples described herein, the values of B are selected from[0,1], where 0 indicates that there is no overlap, and 1 indicates aperfect match.

In some examples, the cavity and myocardium regions in the first frameI¹, denoted respectively by C¹ and M, are provided by a user of theexample diagnostic imaging workstation 105. Based on the exampledefinitions of EQNS (3)-(5), an example cavity/myocardium overlapmeasure is expressed mathematically as

$\begin{matrix}{{\underset{\underset{{{cavity}/{myocardium}}\mspace{14mu}{overlap}\mspace{14mu}{measure}}{︸}}{B^{k} = {B\left( {P_{C^{k},I^{k}}/P_{M,I^{1}}} \right)}}{\forall{k \in \left\lbrack {1,\ldots\mspace{14mu},K} \right\rbrack}}},} & (6)\end{matrix}$where B^(k) represents the amount of overlap between the intensitydistribution within the heart cavity region C^(k) in frame I^(k) and themyocardium model learned from the first frame I¹. In most instances,B^(k) is approximately constant over the cardiac sequence I.Consequently, the value of B¹ estimated from the segmentation of thefirst frame I¹ in the sequence I can be used as an overlap-prior toconstrain the tracking of the boundary cavity in the subsequent framesI², . . . , I^(K). To embed prior information about the overlap betweenthe intensity distribution within the cavity and myocardium, the exampleimage pre-processing module 320 of FIG. 3 minimizes the followingconstraint for each frame kε[2, . . . , K]

$\begin{matrix}{{O^{k} = \underset{\underset{{{cavity}/{myocardium}}\mspace{14mu}{overlap}\mspace{14mu}{prior}}{︸}}{\left( {B_{in}^{k} - B_{in}^{1}} \right)^{2}}},} & (7)\end{matrix}$where O^(k) represents the overlap between the intensity distributionswithin the cavity and prior myocardium fits B_(in) ¹.

An example mean-matching term, which represents conformity of anintensity mean computed for the left-ventricle cavity in the currentframe I^(k) to a mean computed for the first frame I¹, is defined by thefollowing mathematical expression:

$\begin{matrix}{{M^{k} = \underset{\underset{{cavity}\mspace{14mu}{mean}\mspace{14mu}{prior}}{︸}}{\left( {\mu^{k} - \mu^{1}} \right)^{2}}},} & (8)\end{matrix}$where μ^(k) the estimate of intensity mean within C^(k) for kε[1, . . ., K], which is expressed mathematically as

$\begin{matrix}{\mu^{k} = {\frac{\int_{C^{k}}{r^{k}{\mathbb{d}x}}}{a_{C^{k}}}.}} & (9)\end{matrix}$

An example regularization/gradient term, which may be used to bias thecurve toward a high intensity gradient and/or to enforce curvesmoothness, is defined mathematically asG ^(k)=

(g _(k) +c)ds,  (10)where c is a positive constant and g_(k) is an edge indicator function,which is defined as

$\begin{matrix}{g_{k} = {\frac{1}{1 + {{\nabla I^{k}}}^{2}}{\forall{k \in {\left\lbrack {1,\ldots\mspace{14mu},K} \right\rbrack.}}}}} & (11)\end{matrix}$

Based on the example terms defined above in EQNS (3)-(11), an examplecost function F^(k) that may be minimized to identify, compute and/orotherwise determine the parametric curve {right arrow over (Γ)}^(k) isdefined by

$\begin{matrix}\begin{matrix}{F^{k} = {{\alpha\; O^{k}} + {\beta\; M^{k}} + {\lambda\; G^{k}}}} \\{= {\underset{\underset{{{cavity}/{myocardium}}\mspace{14mu}{overlap}\mspace{14mu}{prior}}{︸}}{{\alpha\left( {B^{k} - B^{1}} \right)}^{2}} + \underset{\underset{{cavity}\mspace{14mu}{mean}\mspace{14mu}{matching}}{︸}}{{\beta\left( {\mu^{k} - \mu^{1}} \right)}^{2}} +}} \\{\underset{\underset{{cavity}\mspace{14mu}{boundary}}{︸}}{\lambda{\oint_{{\overset{->}{\Gamma}}^{n}}{\left( {g_{k} + c} \right){\mathbb{d}s}}}},}\end{matrix} & (12)\end{matrix}$where the variables or weights α, β and λ are selected to adjust therelative importance or contribution of the three terms described abovein connection with EQNS (3)-(11).

The example image pre-processing module 320 of FIG. 3 solves for theparametric curve {right arrow over (Γ)}^(k) by minimizing the examplecost function F^(k) of EQN (12) using, for example, Euler-Lagrangedescent minimization. In some examples, the example image pre-processingmodule 320 embeds the curve {right arrow over (Γ)} in a one-parameterfamily of curves: {right arrow over (Γ)}(s,t):[0,1]×R⁺→Ω, and solves thepartial differential equation

$\begin{matrix}{\frac{\partial{{\overset{->}{\Gamma}}^{k}\left( {s,t} \right)}}{\partial t} = {- \frac{\partial F^{k}}{\partial{\overset{->}{\Gamma}}^{k}}}} & (13)\end{matrix}$where

$\frac{\partial F}{\partial\overset{->}{\Gamma}}$denotes the functional derivative of F with respect to {right arrow over(Γ)}. The example expression of EQN (13) can be rewritten as:

$\begin{matrix}{{\frac{\partial{\overset{->}{\Gamma}}^{k}}{\partial t} = {\left\{ {{\frac{\alpha\left( {B^{k} - B^{1}} \right)}{a_{C^{k}}}\left( {B^{k} - \sqrt{\frac{P_{M\;\lambda^{2}}}{P_{C^{k}1^{k}}}}} \right)} + {\frac{2\;{\beta\left( {\mu^{k} - \mu^{2}} \right)}}{a_{C^{k}}}\left( {\mu^{k} - I^{k}} \right)} + {\lambda\left\lbrack {{{\nabla g_{k}} \cdot {\overset{->}{k}}^{k}} - {\left( {g_{k} + c} \right)k^{k}}} \right\rbrack}} \right\}{\overset{->}{k}}^{k}}},} & (14)\end{matrix}$where κ^(k) is the mean curvature function of {right arrow over (Γ)}^(k)and {right arrow over (k)}^(k) is the outward unit normal to {rightarrow over (Γ)}^(k), and assuming that the function K(•) used in thekernel density estimation is the Dirac function. The example imagepre-processing module 320 solves and/or converges the example expressionof EQN (14) for each frame I^(k), with the left-ventricle cavityboundary for frame k given by the thus obtained curve {right arrow over(Γ)}^(k).

While level-set formalisms are used to derive the example curveevolution method described above, any number and/or type(s) ofalternative and/or additional method(s), algorithm(s) and/or formalismsmay be used to obtain the curve {right arrow over (Γ)}^(k) for eachimage I^(k).

While an example manner of implementing the example diagnostic imagingworkstation 105 of FIG. 1 has been illustrated in FIG. 3, one or more ofthe interfaces, data structures, elements, processes and/or devicesillustrated in FIG. 3 may be combined, divided, re-arranged, omitted,eliminated and/or implemented in any other way. The example userinterface(s) 305, the example display(s) 310, the example inputdevice(s) 315, the example image pre-processing module 320, the exampleimage processing module 325 and/or, more generally, the examplediagnostic imaging workstation 105 of FIG. 3 may be implemented byhardware, software, firmware and/or any combination of hardware,software and/or firmware. Thus, for example, any of the example userinterface(s) 305, the example display(s) 310, the example inputdevice(s) 315, the example image pre-processing module 320, the exampleimage processing module 325 and/or, more generally, the examplediagnostic imaging workstation 105 may be implemented by one or morecircuit(s), programmable processor(s), application specific integratedcircuit(s) (ASIC(s)), programmable logic device(s) (PLD(s)) and/or fieldprogrammable logic device(s) (FPLD(s)), etc. When any apparatus claim ofany patent resulting from this non-provisional application is read tocover a purely software and/or firmware implementation, at least one ofthe example user interface(s) 305, the example display(s) 310, theexample input device(s) 315, the example image pre-processing module320, the example image processing module 325 and/or, more generally, theexample diagnostic imaging workstation 105 are hereby expressly definedto include a tangible computer-readable medium such as a memory, a DVD,a CD, etc. storing the firmware and/or software. Further still, theexample diagnostic imaging workstation 105 may include interfaces, datastructures, elements, processes and/or devices instead of, or inaddition to, those illustrated in FIG. 3 and/or may include more thanone of any or all of the illustrated interfaces, data structures,elements, processes and/or devices.

FIG. 4 illustrates an example manner of implementing the example imageprocessing module 325 of FIG. 3. To compute filter coefficients and/orparameters of a state model that predicts the future position and/ormovement of left ventricular cavity points, the example image processingmodule 325 of FIG. 4 includes a motion estimator 405. The example motionestimator 405 of FIG. 4 predicts left-ventricular cavity points byapplying a Bayesian filter, such as the Kalman filter to a sequence ofsegmented left-ventricle cardiac images.

Let (x, y) be a Cartesian point on the endocardial boundary {right arrowover (Γ)}^(k)(s) identified and/or determined by the example imagepre-processing module 320, as described above. Let ξ be an example statevector τ=[ x x {grave over (x)}]^(T) that represents the dynamics of thepoint in the x-coordinate direction, where {grave over (x)} and xdenote, respectively, the velocity and the mean position of the pointover a cardiac cycle or heartbeart. Assuming motion of the heart issubstantially periodic, an example continuous state-space model thatdescribes the cyclic motion of the point can be expressed as

$\begin{matrix}{{{\xi(t)} = {{{\begin{bmatrix}0 & 0 & 0 \\0 & 0 & 1 \\\omega^{2} & {- \omega^{2}} & 0\end{bmatrix}{\xi(t)}} + {\begin{bmatrix}1 & 0 \\0 & 0 \\0 & 1\end{bmatrix}{w(t)}}} = {{{A(t)}{\xi(t)}} + {{Bw}(t)}}}},} & (15)\end{matrix}$where ω is the angular frequency, and w(t) is white noise thatrepresents the unpredictable modeling errors arising in heart motiondetection. The example mathematical model of EQN (15) is linear for agiven ω, and is an approximation of a temporal periodic model wherehigher-order terms of the Fourier expansion are neglected. Asubstantially equivalent discrete-time version of EQN (15) can beexpressed as

$\begin{matrix}\begin{matrix}{\xi_{k + 1} = {{\begin{bmatrix}1 & 0 & 0 \\{1 - {\cos\left( {\omega\; T} \right)}} & {\cos\left( {\omega\; T} \right)} & {\frac{1}{\omega}{\sin\left( {\omega\; T} \right)}} \\{\omega\;{\sin\left( {\omega\; T} \right)}} & {{- \omega}\;{\sin\left( {\omega\; T} \right)}} & {\cos\left( {\omega\; T} \right)}\end{bmatrix}\xi_{k}} + w_{k}}} \\{{= {{{F_{cy}(k)}\xi_{k}} + w_{k}}},}\end{matrix} & (16)\end{matrix}$where the covariance of the process noise Q_(k)=cov(w_(k)) is given byQ _(k) =[q _(ij)]_(3×),  (17)and the q_(ij)'s are defined to be

$\begin{matrix}{\mspace{79mu}{q_{11} = {q_{1}^{2}T}}} & (18) \\{\mspace{79mu}{q_{12} = {q_{21} = \frac{q_{1}^{2}\left( {{\omega\; T} - {\sin\left( {\omega\; T} \right)}} \right)}{\omega}}}} & (19) \\{\mspace{79mu}{q_{13} = {q_{31} = {q_{1}^{2}\left( {1 - {\cos\left( {\omega\; T} \right)}} \right)}}}} & (20) \\{\mspace{79mu}{q_{22} = {\frac{1}{2}\frac{\begin{matrix}{{q_{1}^{2}{\omega^{2}\left( {{3\;\omega\; T} - {4\;{\sin\left( {\omega\; T} \right)}} + {{\cos\left( {\omega\; T} \right)}{\sin\left( {\omega\; T} \right)}}} \right)}} +} \\{q_{3}^{2}\left( {{\omega\; T} - {{\cos\left( {\omega\; T} \right)}{\sin\left( {\omega\; T} \right)}}} \right)}\end{matrix}}{\left( \omega^{2} \right)}}}} & (21) \\{q_{23} = {q_{32} = {\frac{1}{2}\frac{{q_{1}^{2}{\omega^{2}\left( {1 - {2\;{\cos\left( {\omega\; T} \right)}} + {\cos^{2}\left( {\omega\; T} \right)}} \right)}} + {q_{2}^{2}{\sin^{2}\left( {\omega\; T} \right)}}}{\omega^{2}}}}} & (22) \\{q_{33} = {{- \frac{1}{2}}{\frac{{q_{1}^{2}{\omega^{2}\left( {{{\cos\left( {\omega\; T} \right)}{\sin\left( {\omega\; T} \right)}} - {\omega\; T}} \right)}} - {q_{2}^{2}\left( {{{\cos\left( {\omega\; T} \right)}{\sin\left( {\omega\; T} \right)}} - {\omega\; T}} \right)}}{\omega}.}}} & (23)\end{matrix}$

Letting s represent an example state vector s=[ x x {dot over (x)} y y{dot over (y)}]^(T) representing the dynamics of the left-ventriclecavity in the x-y plane, an example discrete state-space model for themotion of the left-ventricle in the x-y plane is given by

$\begin{matrix}{s_{k + 1} = {{{\begin{bmatrix}{F_{cy}(k)} & 0_{3 \times 3} \\0_{3 \times 3} & {F_{cy}(k)}\end{bmatrix}s_{k}} + v_{k}} = {{F_{k}s_{k}} + {v_{k}.}}}} & (24)\end{matrix}$

Using any number and/or type(s) of algorithm(s) and/or method(s), theexample motion estimator 405 of FIG. 4 processes the segmented imagesfrom the example image pre-processing module 320 to obtain an estimateof the state vector s. For example, the example motion estimator 405applies a Bayesian filter such as a Kalman filter, which may be used asa state estimator for linear and/or Gaussian systems, to recursivelyupdate an estimate the state vector s. Letting z_(k)=[z_(k,x)z_(k,y)]^(T) represent an estimate of the point (x, y) on theendocardial boundary {right arrow over (Γ)}^(k)(s) for frame kε[1, . . ., K], an example measurement equation is given byz _(k) =H _(k) s _(k)+ν_(k),  (25)where

$\begin{matrix}{H_{k} = \begin{bmatrix}0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0\end{bmatrix}} & (26)\end{matrix}$and ν_(k) is a zero-mean Gaussian noise sequence with covariance

$\begin{matrix}{R_{k} = {\begin{bmatrix}r & 0 \\0 & r\end{bmatrix}.}} & (27)\end{matrix}$

The example motion estimator 405 computes a predicted state using theexample model of EQN (24) and by taking an expectation conditioned onz_(1:k)={z₁, . . . , z_(k)}. Letting m_(k)=E[s_(k)] be the mean of thestate vector, the motion estimator 405 computes the predicted stateusing the following mathematical expressionm _(k+1) ⁻ =F _(k) m _(k).  (28)The corresponding state prediction covariance is given byP _(k+1) ⁻ =F _(k) P _(k) ^(F) _(k) ^(T) +Q _(k).  (29)

The example motion estimator 405 of FIG. 4 computes the measurementresidual or innovation by taking the expectation conditioned on z_(1:k)v _(k+1) =z _(k) −H _(k) m _(k+1) ⁻,  (30)with the corresponding innovation covariance defined byS _(k+1) =H _(k) P _(k+1) ⁻ H _(k) ^(T) +R _(k)  (31)and the filter gain given byW _(k+1) =P _(k+1) ⁻ S _(k+1) ⁻¹.  (32)

The motion estimator 405 computes the updated state estimate using thefollowing expressionM _(k+1) =m _(k+1) ⁻ +W _(k+1)ν_(k+1).  (33)The motion estimator 405 computes the updated state covariance using thefollowing mathematical expressionP _(k+1) =P _(k+1) ⁻ −W _(k+1) S _(k+1) W _(k+1) ^(T).  (34)

In some examples, the initial state vector s₁ may not be know a priori.In such examples, the example motion estimator 405 of FIG. 4 implementsa two-point differencing method to initialize position and velocitycomponents of the state vector s. For instance, the motion estimator 405may compute the initial position and velocity elements in x-coordinatedirection using the following equations

$\begin{matrix}{{{\hat{x}}_{1} = z_{1,x}},{and}} & (35) \\{{\hat{\overset{.}{x}}}_{1} = {\frac{\left( {z_{2,x} - z_{1,x}} \right)}{T}.}} & (36)\end{matrix}$The mean position x over the cardiac cycle may be computed by the motionestimator 405 by taking an expectation over all correspondingmeasurements:

$\begin{matrix}{{\hat{\overset{\_}{x}}}_{1} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}z_{k,x}}}} & (37)\end{matrix}$The example motion estimator 405 likewise computes the initial stateelements in y-coordinate direction, ŷ₁, {dot over (ŷ)}₁, and ŷ ₁ usingthe measurements {z_(k,y)}. The motion estimator 405 computes thecorresponding initial covariance by computing the following mathematicalexpression

$\begin{matrix}{{P_{1} = \begin{bmatrix}\Phi_{1} & 0_{3 \times 3} \\0_{3 \times 3} & \Phi_{1}\end{bmatrix}},{where}} & (38) \\{\Phi_{1} = {\begin{bmatrix}r & \frac{r}{K} & \frac{r}{KT} \\\frac{r}{K} & r & \frac{r}{T} \\\frac{r}{KT} & \frac{r}{T} & \frac{2\; r}{T^{2}}\end{bmatrix}.}} & (39)\end{matrix}$

In some instances, segmentation of the left-ventricle cavity may not beconsistent over a cardiac cycle. The example motion estimator 405 ofFIG. 4 detects such inconsistencies by gating the center of thesegmented left-ventricle cavity. For example, letting {s_(k) ^(i)=[ x_(k) ^(i) x_(k) ^(i) {dot over (x)}_(k) ^(i) y _(k) ^(i) y_(k) ^(i) {dotover (y)}_(k) ^(i)]^(T):i=1, . . . , N} be a sample point on theleft-ventricle boundary in frame k, the center of the left-ventriclecavity (c_(x,k) c_(y,k)) may be computed by the motion estimator 405using the following equation:

$\begin{matrix}\left\{ \begin{matrix}{c_{x,k} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}x_{k}^{i}}}} \\{c_{y,k} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{y_{k}^{i}.}}}}\end{matrix} \right. & (40)\end{matrix}$

If √{square root over((c_(x,k+1)−c_(x,k))²+(c_(y,k+1)−c_(y,k))²)}{square root over((c_(x,k+1)−c_(x,k))²+(c_(y,k+1)−c_(y,k))²)}>g (where g is a predefinedconstant), the motion estimator 405 ignores the segmentation results. Insuch instances, the motion estimator 405 only predicts the sample pointsusing the model of EQN (24) without updating the Kalman filter.

In order to identify a sequence of corresponding points over time, theexample motion estimator 405 determines symmetric nearest-neighborcorrespondences by sampling a set of equally-spaced points along theleft-ventricle boundary. The selected sequence of points may be used toanalyze wall motion regionally. For example, using spline interpolation,the motion estimator 405 samples N_(s) points along the left-ventriclecavity in each frame, and N points are chosen as inputs for the Kalmanfilter. The motion estimator 405 computes a kernel density estimationbased on the Gaussian kernel to obtain the probability density. Themotion estimator 405 may normalize the radial distance for each datasetwith respect to maximum value, to analyze different long-axis segments,namely, apical, mid and basal, without additional processing.

To characterize the motion of the heart, the example image processingmodule 325 includes an information metric processor 410. The exampleinformation metric processor 410 of FIG. 4 processes the state modeland/or filter coefficients computed by the example motion estimator 405to compute, estimate and/or otherwise determine one or moreinformation-theoretic measures or metrics representative of heartmotion. Consistent with industry usage, the terms “information-theoreticmetric” and “information-theoretic measures” used herein refer to anyvalues that are computed based on one or more properties of informationtheory. As is well known, the field of information theory is based onprobability theory and statistics, and is concerned with thequantification of information and/or the computation of measures ofinformation. Example information-theoretic metrics are entropy, which isthe information in a random variable, and mutual information, whichrepresents the amount of information in common between two randomvariables. Additional example information-theoretic metrics include, butare not limited to, the Shannon differential entropy (SDE), whichprovides a global theoretical ground measure of distributions, the Rényientropy, and/or Fisher information.

The example information metric processor 410 of FIG. 4 computes anormalized radial distance r_(k) ^(i), which can be expressedmathematically as

$\begin{matrix}{{r_{k}^{i} = \frac{\sqrt{\left( {{\hat{x}}_{k}^{i} - {\frac{1}{N}{\sum\limits_{i}\;{\hat{x}}_{k}^{i}}}} \right)^{2} + \left( {{\hat{y}}_{k}^{i} - {\frac{1}{N}{\sum\limits_{i}{\hat{y}}_{k}^{i}}}} \right)^{2}}}{\max\limits_{i}\sqrt{\left( {{\hat{x}}_{k}^{i} - {\frac{1}{N}{\sum\limits_{i}\;{\hat{x}}_{k}^{i}}}} \right)^{2} + \left( {{\hat{y}}_{k}^{i} - {\frac{1}{N}{\sum\limits_{i}{\hat{y}}_{k}^{i}}}} \right)^{2}}}},} & (41)\end{matrix}$where {circumflex over (x)}_(x) ^(i) and ŷ_(k) ^(i) are the estimates ofx_(k) ^(i) and x_(k) ^(i), respectively. The values and {circumflex over(x)}_(k) ^(i) ŷ_(k) ^(i) are computed using the Kalman filter describedabove. Letting rε

be a random variable, the example information metric processor 410computes a kernel density estimate of the normalized radial distanceusing the following equation

$\begin{matrix}{{{f(r)} = \frac{\sum\limits_{i,k}{k_{\sigma}\left( {r_{k}^{i} - r} \right)}}{N \times K}},{where}} & (42) \\{{H_{a}(y)} = {\frac{1}{\sqrt{2\;\pi\;\sigma^{2}}}{\exp\left( {- \frac{y^{2}}{2\;\sigma^{2}}} \right)}}} & (43)\end{matrix}$is the Gaussian kernel.

An example SDE computed by the example information metric processor 410of FIG. 4 is defined by the following mathematical expression

$\begin{matrix}{S_{f} = {- {\int_{r \in \overset{\_}{R}}{\frac{\sum\limits_{i,k}{k_{\sigma}\left( {r_{k}^{i} - r} \right)}}{NK}\left( {{\ln\;{\sum\limits_{i,k}{k_{\sigma}\left( {r_{k}^{i} - r} \right)}}} - {\ln\;{NK}}} \right){\mathbb{d}r}}}}} & (44)\end{matrix}$

Other example information-theoretic metrics that may be computed by theexample information metric processor 410 include, but are not limitedto, the Rényi entropy

$\begin{matrix}{R_{f}^{\alpha} = {\frac{1}{1 - \alpha}\ln{\int_{r \in \overset{\_}{R}}{{{{\left. \frac{\sum\limits_{i,k}{k_{a}\left( {r_{k}^{i} - r} \right)}}{NK} \right)^{\alpha}{\mathbb{d}r}0} < \alpha < \infty},{\alpha \neq 1},}}}}} & (45)\end{matrix}$and Fisher informationI _(f)=4∫_(rε)

|

g(r)|² dr,  (46)where

$\begin{matrix}{{g(r)} = \sqrt{\frac{\sum\limits_{i,k}{k_{\sigma}\left( {r_{k}^{i} - r} \right)}}{NK}}} & (47)\end{matrix}$

To classify the motion of the heart, the example image processing module325 includes a classifier 415. The example classifier 415 of FIG. 4compares the information-theoretic metrics computed by the informationmetric processor 410 to one or more thresholds. Based on thecomparison(s), the motion of the heart is classified as normal orabnormal.

While an example manner of implementing the example image processingmodule 325 of FIG. 3 is illustrated in FIG. 4, one or more of theinterfaces, data structures, elements, processes and/or devicesillustrated in FIG. 4 may be combined, divided, re-arranged, omitted,eliminated and/or implemented in any other way. The example motionestimator 405, the example information metric processor 410, the exampleclassifier 415 and/or, more generally, the example image processingmodule 325 of FIG. 4 may be implemented by hardware, software, firmwareand/or any combination of hardware, software and/or firmware. Thus, forexample, any of the example motion estimator 405, the exampleinformation metric processor 410, the example classifier 415 and/or,more generally, the example image processing module 325 may beimplemented by one or more circuit(s), programmable processor(s),ASIC(s), PLD(s) and/or FPLD(s), etc. Any apparatus claim of any patentresulting from this non-provisional application is read to cover apurely software and/or firmware implementation, at least one of theexample motion estimator 405, the example information metric processor410, the example classifier 415 and/or, more generally, the exampleimage processing module 325 are hereby expressly defined to include atangible computer-readable medium such as a memory, a DVD, a CD, etc.storing the firmware and/or software. Further still, the example imageprocessing module 325 may include interfaces, data structures, elements,processes and/or devices instead of, or in addition to, thoseillustrated in FIG. 4 and/or may include more than one of any or all ofthe illustrated interfaces, data structures, elements, processes and/ordevices.

FIG. 5 illustrates an example process that may be carried out toimplement the example image processing module 325 and/or, moregenerally, the example diagnostic workstation 105 of FIGS. 1, 3 and 4.The example process of FIG. 5 may be carried out by a processor, acontroller and/or any other suitable processing device. For example, theexample process of FIG. 5 may be embodied in coded instructions storedon a tangible computer-readable medium such as a flash memory, a CD, aDVD, a floppy disk, a read-only memory (ROM), a random-access memory(RAM), a programmable ROM (PROM), an electronically-programmable ROM(EPROM), and/or an electronically-erasable PROM (EEPROM), an opticalstorage disk, an optical storage device, magnetic storage disk, amagnetic storage device, and/or any other medium which can be used tocarry or store program code and/or instructions in the form ofcomputer-executable instructions or data structures, and which can beaccessed by a processor, a general purpose or special purpose computeror other machine with a processor (e.g., the example processor platformP100 discussed below in connection with FIG. 6). Combinations of theabove are also included within the scope of computer-readable media.Computer-executable instructions comprise, for example, instructions anddata that cause a processor, a general purpose computer, special purposecomputer, or a special purpose processing machine to perform one or moreparticular processes. Alternatively, some or all of the example processof FIG. 5 may be implemented using any combination(s) of ASIC(s),PLD(s), FPLD(s), discrete logic, hardware, firmware, etc. Also, some orall of the example process of FIG. 5 may be implemented manually or asany combination of any of the foregoing techniques, for example, anycombination of firmware, software, discrete logic and/or hardware.Further, many other methods of implementing the example operations ofFIG. 5 may be employed. For example, the order of execution of theblocks may be changed, and/or one or more of the blocks described may bechanged, eliminated, sub-divided, or combined. Additionally, any or allof the example process of FIG. 5 may be carried out sequentially and/orcarried out in parallel by, for example, separate processing threads,processors, devices, discrete logic, circuits, etc.

The example process of FIG. 5 begins with the example diagnostic imagingworkstation 105 collecting a sequence of left-ventricle cardiac imagesfrom the example image manager 120 (block 505). The example imagepre-processing module 320 segments the images (block 510). The examplemotion estimator 405 applies a Kalman filter to generate a model and/orfilter representative of the motion of the segmented imagedleft-ventricle images (block 515). Based on the generated model and/orfilters, the example information metric processor 410 computes one ormore information-theoretic metrics, such as the SDE, the Rényi entropy,and/or the Fisher information (block 520). Based on the computedinformation-theoretic metric(s), the example classifier 415 determineswhether the motion of the imaged heart is normal or abnormal (block525). Control then exits from the example process of FIG. 5.

FIG. 6 is a schematic diagram of an example processor platform P100 thatmay be used and/or programmed to implement any or all of the examplediagnostic imaging workstation 105, the example image pre-processingmodule 320, the example image processing module 325, the example motionestimator 405, the example information metric processor 410, and/or theexample classifier 415 of FIGS. 1, 3 and 4. For example, the processorplatform P100 can be implemented by one or more general-purposeprocessors, processor cores, microcontrollers, etc.

The processor platform P100 of the example of FIG. 6 includes at leastone general-purpose programmable processor P105. The processor P105executes coded instructions P110 and/or P112 present in main memory ofthe processor P105 (e.g., within a RAM P115 and/or a ROM P120). Theprocessor P105 may be any type of processing unit, such as a processorcore, a processor and/or a microcontroller. The processor P105 mayexecute, among other things, the example process of FIG. 5 to implementthe example cardiac left-ventricle image-processing methods andapparatus described herein.

The processor P105 is in communication with the main memory (including aROM P120 and/or the RAM P115) via a bus P125. The RAM P115 may beimplemented by dynamic random access memory (DRAM), synchronous dynamicrandom access memory (SDRAM), and/or any other type of RAM device, andROM may be implemented by flash memory and/or any other desired type ofmemory device. Access to the memory P115 and the memory P120 may becontrolled by a memory controller (not shown). The example memory P115may be used to implement the example image database 115 of FIG. 1.

The processor platform P100 also includes an interface circuit P130. Theinterface circuit P130 may be implemented by any type of interfacestandard, such as an external memory interface, serial port,general-purpose input/output, etc. One or more input devices P135 andone or more output devices P140 are connected to the interface circuitP130. The input devices P135 may be used to, for example, implement theexample input device(s) 315 of FIG. 3. The example output devices P140may be used to, for example, implement the example display 310 of FIG.3.

Generally, computer-executable instructions include routines, programs,objects, components, data structures, etc., that perform particulartasks or implement particular abstract data types. Computer-executableinstructions, associated data structures, and program modules representexamples of program code for executing the processes to implement theexample methods and systems disclosed herein. The particular sequence ofsuch executable instructions and/or associated data structures representexamples of corresponding acts for implementing the examples describedherein.

The example methods and apparatus described herein may be practiced in anetworked environment using logical connections to one or more remotecomputers having processors. Logical connections may include a localarea network (LAN) and a wide area network (WAN) that are presented hereby way of example and not limitation. Such networking environments arecommonplace in office-wide or enterprise-wide computer networks,intranets and the Internet and may use a wide variety of differentcommunication protocols. Such network computing environments mayencompass many types of computer system configurations, includingpersonal computers, hand-held devices, multi-processor systems,microprocessor-based or programmable consumer electronics, network PCs,minicomputers, mainframe computers, and the like. The example methodsand apparatus described herein may, additionally or alternatively, bepracticed in distributed computing environments where tasks areperformed by local and remote processing devices that are linked (eitherby hardwired links, wireless links, or by a combination of hardwired orwireless links) through a communications network. In a distributedcomputing environment, program modules may be located in both local andremote memory storage devices.

Although certain example methods, apparatus and articles of manufacturehave been described herein, the scope of coverage of this patent is notlimited thereto. On the contrary, this patent covers all methods,apparatus and articles of manufacture fairly falling within the scope ofthe appended claims either literally or under the doctrine ofequivalents.

What is claimed is:
 1. A method comprising: using a filter to estimate astate vector representative of motion of a heart based on a plurality ofcardiac images; computing, via a processor, an information-theoreticmetric based on the estimated state vector; and comparing theinformation-theoretic metric to a threshold to determine whether themotion of the heart is abnormal.
 2. A method as defined in claim 1,wherein the information-theoretic metric comprises a Shannondifferential entropy.
 3. A method as defined in claim 1, wherein theinformation-theoretic metric comprises a Rényi entropy.
 4. A method asdefined in claim 1, wherein the information-theoretic metric comprisesFisher information.
 5. A method as defined in claim 1, wherein computingthe information-theoretic metric comprises: computing a kernel densityestimate of a normalized radial distance; and computing theinformation-theoretic metric from the kernel density estimate.
 6. Amethod as defined in claim 1, further comprising segmenting theplurality of cardiac images to form respective ones of a plurality ofsegmented cardiac images, wherein the filter is adapted based on theplurality of segmented cardiac images.
 7. A non-transitorycomputer-readable storage device storing machine-readable instructionsthat, when executed, cause a machine to: use a filter to estimate astate vector representative of motion of a heart based on a plurality ofcardiac images; compute an information-theoretic metric based on theestimated state vector; and compare the information-theoretic metric toa threshold to determine whether the motion of the heart is abnormal. 8.A non-transitory computer-readable storage device as defined in claim 7,wherein the information-theoretic metric comprises a Shannondifferential entropy.
 9. A non-transitory computer-readable storagedevice as defined in claim 7, wherein the information-theoretic metriccomprises a Rényi entropy.
 10. A non-transitory computer-readablestorage device as defined in claim 7, wherein the information-theoreticmetric comprises Fisher information.
 11. A non-transitorycomputer-readable storage device as defined in claim 7, wherein themachine-readable instructions, when executed, cause the machine tosegment the plurality of cardiac images to form respective ones of aplurality of segmented cardiac images, wherein the filter is adaptedbased on the plurality of segmented cardiac images.
 12. A non-transitorycomputer-readable storage device as defined in claim 7, wherein themachine-readable instructions, when executed, cause the machine tocompute the information-theoretic metric by: computing a kernel densityestimate of a normalized radial distance; and computing theinformation-theoretic metric from the kernel density estimate.
 13. Anapparatus comprising: a motion estimator to, using a filter, estimate astate vector representative of motion of a heart based on a plurality ofcardiac images; an information metric processor to compute aninformation-theoretic metric based on the estimated state vector; and aclassifier to compare the information-theoretic metric to a threshold todetermine whether the motion of the heart is abnormal.
 14. An apparatusas defined in claim 13, further comprising an imaging device to capturethe plurality of cardiac images of the heart.
 15. An apparatus asdefined in claim 13, further comprising an image pre-processor tosegment the plurality of cardiac images to form respective ones of aplurality of segmented cardiac images, wherein the filter is adaptedbased on the plurality of segmented cardiac images.
 16. An apparatus asdefined in claim 13, wherein the filter comprises at least one of aBayesian filter or a Kalman filter.
 17. An apparatus as defined in claim13, wherein the information-theoretic metric comprises a Shannondifferential entropy.
 18. An apparatus as defined in claim 13, whereinthe information-theoretic metric comprises a Rényi entropy.
 19. Anapparatus as defined in claim 13, wherein the information-theoreticmetric comprises Fisher information.
 20. An apparatus as defined inclaim 13, wherein the information metric processor is to compute theinformation-theoretic metric by: computing a kernel density estimate ofa normalized radial distance; and computing the information-theoreticmetric from the kernel density estimate.